How do I know when I am hearing classical music?

Question:
"How do I know when I am hearing classical music?"

Answer:
You won't know for sure. "Classical music" is a definition, it is not the thing that people do. What you can learn to recognise is certain accepted styles which are agreed upon as being classical music.

And nobody would argue with that. Where they will argue is on precisely how that piece should be played. Some will argue about how Mozart played it. Some will argue about how he meant to play it, but never did, exactly.

As you are gathering, there is vast scope for disputation here, and there are many careers built on trying to clarify these issues, which is a commendable thing, or to promulgate a dogmatic attitude about how the music must be played, which is not such a commendable thing.